Practice · Maths AI SL · 2021 syllabus · 4.11
IB Maths AI SL 4.11 Hypothesis tests: chi-squared and t-test: practice questions
2 exam-style questions on 4.11 Hypothesis tests: chi-squared and t-test, SL: 2 Paper 1 short. Each one comes with the mark scheme, a model answer and the reasoning behind every mark. Free with an account.
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4.11-01 · Paper 1 style · short question · 5 marks
Membership type and activity
A sports centre asked 150 of its members which activity they use most often. The table shows their replies by type of membership.
| Membership | Swimming | Gym | Classes | Total |
|---|---|---|---|---|
| Student | 12 | 21 | 9 | 42 |
| Adult | 19 | c | 17 | 62 |
| Senior | 20 | 9 | 17 | 46 |
| Total | 51 | 56 | 43 | 150 |
(a) Write down the value of \(c\). [1]
The centre tests, at the 5% significance level, whether the most-used activity depends on the type of membership.
\(H_0\): membership type and most-used activity are independent.
\(H_1\): membership type and most-used activity are not independent.
At this level the critical value is 9.488.
(b) Find the \(\chi^2\) statistic for this test. [2]
(c) State the centre's conclusion in context, with a reason. [2]
Show the answer and the reasoning
(a) Mark scheme
- A1 \(c = 26\);
A model answer: Adult row: \(19 + c + 17 = 62\), so \(c = 26\).
(b) Mark scheme
- (M1) the observed values entered as a 3 by 3 table, totals left out (implied by a correct answer);
- A1 \(\chi^2_{\text{calc}} = 9.74\) (9.73536...);
A model answer: The nine observed values go into the GDC as a 3 by 3 matrix: \(\chi^2_{\text{calc}} = 9.74\) (9.73536...), with 4 degrees of freedom and \(p = 0.0451\).
(c) Mark scheme
- R1 \(9.74 > 9.488\) OR \(p = 0.0451 \lt 0.05\), with both numbers stated;
- A1 reject \(H_0\): there is sufficient evidence that the most-used activity depends on the type of membership;
A model answer: \(9.74 > 9.488\), so we reject \(H_0\). At the 5% level there is sufficient evidence that membership type and most-used activity are not independent.
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The 2 questions in 4.11
- 4.11-01 Membership type and activity
- 4.11-02 Battery life t-test
More of 4 Statistics and probability
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Every Maths question here is original, each one modelled on a question from the AI SL or AA SL papers set since 2021, with a new context and new numbers. Developed independently from the International Baccalaureate Organization, which has not endorsed it. Found a mistake? Email vytis@limeadmissions.com with the question id.